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Simplifying (4x3 + -6x2 + 8x) + (7x3 + 9x2 + -13x) = 0 Reorder the terms: (8x + -6x2 + 4x3) + (7x3 + 9x2 + -13x) = 0 Remove parenthesis around (8x + -6x2 + 4x3) 8x + -6x2 + 4x3 + (7x3 + 9x2 + -13x) = 0 Reorder the terms: 8x + -6x2 + 4x3 + (-13x + 9x2 + 7x3) = 0 Remove parenthesis around (-13x + 9x2 + 7x3) 8x + -6x2 + 4x3 + -13x + 9x2 + 7x3 = 0 Reorder the terms: 8x + -13x + -6x2 + 9x2 + 4x3 + 7x3 = 0 Combine like terms: 8x + -13x = -5x -5x + -6x2 + 9x2 + 4x3 + 7x3 = 0 Combine like terms: -6x2 + 9x2 = 3x2 -5x + 3x2 + 4x3 + 7x3 = 0 Combine like terms: 4x3 + 7x3 = 11x3 -5x + 3x2 + 11x3 = 0 Solving -5x + 3x2 + 11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 3x + 11x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-5 + 3x + 11x2)' equal to zero and attempt to solve: Simplifying -5 + 3x + 11x2 = 0 Solving -5 + 3x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.4545454545 + 0.2727272727x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + 0.2727272727x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + 0.2727272727x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + 0.2727272727x + x2 = 0 + 0.4545454545 0.2727272727x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 0.2727272727x + x2 = 0.4545454545 The x term is 0.2727272727x. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727x + 0.01859504133 + x2 = 0.4545454545 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727x + x2 = 0.4545454545 + 0.01859504133 Combine like terms: 0.4545454545 + 0.01859504133 = 0.47314049583 0.01859504133 + 0.2727272727x + x2 = 0.47314049583 Factor a perfect square on the left side: (x + 0.1363636364)(x + 0.1363636364) = 0.47314049583 Calculate the square root of the right side: 0.687852089 Break this problem into two subproblems by setting (x + 0.1363636364) equal to 0.687852089 and -0.687852089.Subproblem 1
x + 0.1363636364 = 0.687852089 Simplifying x + 0.1363636364 = 0.687852089 Reorder the terms: 0.1363636364 + x = 0.687852089 Solving 0.1363636364 + x = 0.687852089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = 0.687852089 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = 0.687852089 + -0.1363636364 x = 0.687852089 + -0.1363636364 Combine like terms: 0.687852089 + -0.1363636364 = 0.5514884526 x = 0.5514884526 Simplifying x = 0.5514884526Subproblem 2
x + 0.1363636364 = -0.687852089 Simplifying x + 0.1363636364 = -0.687852089 Reorder the terms: 0.1363636364 + x = -0.687852089 Solving 0.1363636364 + x = -0.687852089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = -0.687852089 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = -0.687852089 + -0.1363636364 x = -0.687852089 + -0.1363636364 Combine like terms: -0.687852089 + -0.1363636364 = -0.8242157254 x = -0.8242157254 Simplifying x = -0.8242157254Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5514884526, -0.8242157254}Solution
x = {0, 0.5514884526, -0.8242157254}
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